Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  vd23 Structured version   Visualization version   GIF version

Theorem vd23 38295
Description: A virtual deduction with 2 virtual hypotheses virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same 2 virtual hypotheses and a third hypothesis. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
vd23.1 (   𝜑   ,   𝜓   ▶   𝜒   )
Assertion
Ref Expression
vd23 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜒   )

Proof of Theorem vd23
StepHypRef Expression
1 vd23.1 . . . 4 (   𝜑   ,   𝜓   ▶   𝜒   )
21dfvd2i 38269 . . 3 (𝜑 → (𝜓𝜒))
32a1dd 50 . 2 (𝜑 → (𝜓 → (𝜃𝜒)))
43dfvd3ir 38277 1 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  (   wvd2 38261  (   wvd3 38271
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1038  df-vd2 38262  df-vd3 38274
This theorem is referenced by:  e23  38450  e32  38453  e123  38457
  Copyright terms: Public domain W3C validator